The transient thermal stress problem in a hollow cylinder or a disk containing a radial crack is considered. It is assumed that the cylinder is reinforced on its inner boundary by a membrane which has thermoelastic constants different than those of the base material. The transient temperature, thermal stresses and the crack tip stress intensity factors are calculated in a cylinder which is subjected to a sudden change of temperature on the inside surface. The results are obtained for various dimensionless parameters and material constants. The special cases of the crack terminating at the cylinder-membrane interface and of the broken membrane are separately considered and some examples are given.